Events

Diagnostics for Regression Models with Discrete Outcomes

Making informed decisions about model adequacy has been an outstanding issue for regression models with discrete outcomes. Standard residuals such as Pearson and deviance residuals for such outcomes often show a large discrepancy from the hypothesized pattern even under the true model and are not informative especially when data are highly discrete. To fill this gap, we propose a surrogate empirical residual distribution function for general discrete (e.g. ordinal and count) outcomes that serves as an alternative to the empirical Cox-Snell residual distribution function. When at least one continuous covariate is available, we show asymptotically that the proposed function converges uniformly to the identity function under the correctly specified model, even with highly discrete (e.g. binary) outcomes. Through simulation studies, we demonstrate empirically that the proposed surrogate empirical residual distribution function is highly effective for various diagnostic tasks, since it is close to the hypothesized pattern under the true model and significantly departs from this pattern under model misspecification.

The possibility of nearly assumption-free inference in causal inference

In causal effect estimation, the state-of-the-art is the so-called double machine learning (DML) estimators, which combine the benefit of doubly robust estimation, sample splitting and using machine learning methods to estimate nuisance parameters. The validity of the confidence interval associated with a DML estimator, in most part, relies on the complexity of nuisance parameters and how close the machine learning estimators are to the nuisance parameters. Before we have a complete understanding of the theory of many machine learning methods including deep neural networks, even a DML estimator may have a bias so large that prohibits valid inference. In this talk, we describe a nearly assumption-free procedure that can either criticize the invalidity of the Wald confidence interval associated with the DML estimators of some causal effect of interest or falsify the certificates (i.e. the mathematical conditions) that, if true, could ensure valid inference. Essentially, we are testing the null hypothesis that if the bias of an estimator is smaller than a fraction $\rho$ its standard error. Our test is valid under the null without requiring any complexity (smoothness or sparsity) assumptions on the nuisance parameters or the properties of machine learning estimators and may have power to inform the analysts that they have to do something else than DML estimators or Wald confidence intervals for inference purposes. This talk is based on joint work with Rajarshi Mukherjee and James M. Robins.

Clustering and Classification of Three-Way Data

Clustering and classification is the process of finding and analyzing underlying group structure in heterogenous data and is fundamental to computational statistics and machine learning. In the past, relatively simple techniques could be used for clustering; however, with data becoming increasingly complex, these methods are oftentimes not advisable, and in some cases not possible. One such such example is the analysis of three-way data where each data point is represented as a matrix instead of a traditional vector. Examples of three-way include greyscale images and multivariate longitudinal data. In this talk, recent methods for clustering three-way data will be presented including high-dimensional and skewed three-way data. Both simulated and real data will be used for illustration and future directions and extensions will be discussed.

Batch-mode active learning for regression and its application to the valuation of large variable annuity portfolios

Supervised learning algorithms require a sufficient amount of labeled data to construct an accurate predictive model. In practice, collecting labeled data may be extremely time-consuming while unlabeled data can be easily accessed. In a situation where labeled data are insufficient for a prediction model to perform well and the budget for an additional data collection is limited, it is important to effectively select objects to be labeled based on whether they contribute to a great improvement in the model's performance. In this talk, I will focus on the idea of active learning that aims to train an accurate prediction model with minimum labeling cost. In particular, I will present batch-mode active learning for regression problems. Based on random forest, I will propose two effective random sampling algorithms that consider the prediction ambiguities and diversities of unlabeled objects as measures of their informativeness. Empirical results on an insurance data set demonstrate the effectiveness of the proposed approaches in valuing large variable annuity portfolios (which is a practical problem in the actuarial field). Additionally, comparisons with the existing framework that relies on a sequential combination of unsupervised and supervised learning algorithms are also investigated.

Detecting the Signal Among Noise and Contamination in High Dimensions

Improvements in biomedical technology and a surge in other data-driven sciences lead to the collection of increasingly large amounts of data. In this affluence of data, contamination is ubiquitous but often neglected, creating substantial risk of spurious scientific discoveries. Especially in applications with high-dimensional data, for instance proteomic biomarker discovery, the impact of contamination on methods for variable selection and estimation can be profound yet difficult to diagnose.

In this talk I present a method for variable selection and estimation in high-dimensional linear regression models, leveraging the elastic-net penalty for complex data structures. The method is capable of harnessing the collected information even in the presence of arbitrary contamination in the response and the predictors. I showcase the method’s theoretical and practical advantages, specifically in applications with heavy-tailed errors and limited control over the data. I outline efficient algorithms to tackle computational challenges posed by inherently non-convex objective functions of robust estimators and practical strategies for hyper-parameter selection, ensuring scalability of the method and applicability to a wide range of problems.

Censoring Unbiased Regression Trees and Ensembles

Tree-based methods are useful tools to identify risk groups and conduct prediction by employing recursive partitioning to separate subjects into different risk groups. We propose a novel paradigm of building regression trees for censored data in survival analysis. We prudently construct the censored-data loss function through an extension of the theory of censoring unbiased transformations. With the construction, we can conveniently implement the proposed regression trees algorithm using existing software for the Classification and Regression Trees algorithm (e.g., rpart package in R) and extend it for ensemble learning. Simulations and real data examples demonstrate that our methods either improve upon or remain competitive with existing tree-based algorithms for censored data.

The Extended Reproducibility Phenotype - Re-framing and Generalizing Computational Reproducibility

Computational reproducibility has become a crucial part of how data analytic results are understood and assessed both in and outside of academia. Less work, however, has explored whether these strict computational reproducibility criteria are necessary or sufficient to actually meet our needs as consumers of analysis results. I will show that in principle they are neither. I will present two inter-related veins of work. First, I will provide a  conceptual reframing of the concepts of strict reproducibility, and the actions analysts take to ensure it, in terms of our ability to actually trust the results and the claims about the underlying data-generating systems they embody. Second, I will present a generalized conception of reproducibily by introducing the concepts of Currency, Comparability and Completeness and their oft-overlooked importance to assessing data analysis results.

Please note: This seminar has been cancelled.

Network Response Regression for Modeling Population of Networks with Covariates

Multiple-network data are fast emerging in recent years, where a separate network over a common set of nodes is measured for each individual subject, along with rich subject covariates information. Existing network analysis methods have primarily focused on modeling a single network, and are not directly applicable to multiple networks with subject covariates.

In this talk, we present a new network response regression model, where the observed networks are treated as matrix-valued responses, and the individual covariates as predictors. The new model characterizes the population-level connectivity pattern through a low-rank intercept matrix, and the parsimonious effects of subject covariates on the network through a sparse slope tensor. We formulate the parameter estimation as a non-convex optimization problem, and develop an efficient alternating gradient descent algorithm. We establish the non-asymptotic error bound for the actual estimator from our optimization algorithm. Built upon this error bound, we derive the strong consistency for network community recovery, as well as the edge selection consistency. We demonstrate the efficacy of our method through intensive simulations and two brain connectivity studies.

Join Zoom Meeting

Meeting ID: 844 283 6948
Passcode: 318995

Please Note: This seminar will be given online.

A Marked Spatial Point Process for Insurance Claims Management